RAD (or eclipse) plug-in

I use RAD 8. In one workspace, I used "help->install new software" and added a plug-in. Then I created a new workspace, in the new workspace, I thought I needed to install this new software again. So I did the same thing "help-> install new software " and input the same URL, and click next, it started installing and at the end it gave error. Then I clicked 'what's already installed" and found it is already there. My questions are

1) Is it true that if I install one plug-in in one workspace, then in any new workspace that plug-in is automatically there and we don't need to install it again ? If this is true, how can this plug-in be "carried" from one workspace to another new workspace ? Please help explain little bit.

2) As I said, in the new workspace, I tried to install the same plkug-in software again, and it started all the way till end and gave me error saying it can't complete. If this error is caused by the fact that it can't install something is already there, then does this second attempt of install cause any problem ? i.e. If this extra install attemp causes trouble, maybe I need to uninstall this plug-in and install it again ?

Although this is RAD question, I believe it applies to eclipse as well since RAD is built on top of eclipse.

In eclipse, a workspace only contains your source code and a .metadata folder that keeps history of your view and workbench settings. It doesn't contain installed plugins.
Plugins go into subfolders of the eclipse home folder.
So when you switch workspaces you still have the same plugins because you are still using the same eclipse installation with the same plugins folder. You just lose your workbench settings because they were saved in a different workspace location.